Why are there SEC net capital requirements for brokers?

When a customer uses margin for trading, Reg T dictates the amount he can use and the extent to which the value his market position can decrease until he is required requires additional money. Otherwise, the broker liquidates the position. The Net Capital Rule is analogous in that it dictates how much 'margin' (as in assets) the broker must maintain in order to continue operating:

Net Capital Rule (Rule 15c3-1) – Requires a broker-dealer to maintain more than a dollar of highly liquid assets for each dollar of liabilities. If the broker-dealer fails, this rule helps to ensure that the broker-dealer has sufficient liquid assets to pay all liabilities to customers.

And yes, customer funds and securities must be segregated from the firm’s proprietary business activities. The assets cannot be commingled and used for company purposes. So if the company goes out of business, customer assets can be given back to them. This regulation is the Customer Protection Rule (Rule 15c3-3):

Broker-dealers sometime use their own funds to conduct trades and other transactions. Rule 15c3-3 essentially requires a broker-dealer that maintains custody of customer securities and cash to segregate such securities and cash from the broker-dealer’s proprietary activities. By segregating customer securities and cash from a firm’s proprietary business activities, the rule increases the likelihood that customer assets will be readily available to be returned to customers if a broker-dealer fails.